This proposal outlines a series of experiments designed to investigate the nature of internal representation of external visual objects and of spatial transformations performed upon such objects. Specific factors to be investigated include (a) the effect of two-dimensional visual complexity upon the time required to perform mental transformations, and (b) the effect of the dimensional structure of a visual object upon transformation time. The experimental methods to be used involved measuring response times. New techniques are introduced which (a) permit the measurement of two reaction times on each experimental trial -- the time required to perform preparatory mental transformations in the absence of an external test stimulus, and the time required to respond discriminatively to the test stimulus when it physically appears, and (b) provide an indication of the degree of isomorphism between the spatial structure of an external visual object and that of its corresponding transformed internal representation. The long-range goal of the proposed research is to clarify the nature of the processes by which we represent to ourselves, internally, visual objects and events by placing constraints upon the sorts of models which can be used to describe such internal processes and representations.